@article {IOPORT.01578881,
author = {Br\"oker, Markus and Zhou, Xinlong},
title = {Characterization of continuous, four-coefficient scaling functions via matrix spectral radius.},
year = {2000},
journal = {SIAM Journal on Matrix Analysis and Applications},
volume = {22},
number = {1},
issn = {0895-4798},
pages = {242-257},
publisher = {Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA},
doi = {10.1137/S0895479897323750},
abstract = {Summary: We characterize the existence of continuous solutions of a four-coefficient dilation equation in terms of the usual spectral radius of a matrix. The criteria for the existence of such a solution can be very quickly examined. As a result we give an affirmative answer to a conjecture raised by {\it D. Colella} and {\it C. Heil} in 1992 [IEEE Trans. Inf. Theory 38, No. 2/II, 876-881 (1992; Zbl 0743.42012)]. Moreover, using our criteria we find the smoothest compactly supported four-coefficient orthogonal scaling function and thus the smoothest compactly supported orthonormal wavelet generated by this scaling function.},
identifier = {01578881},
}